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Certain groups with bounded movement having the maximal number of orbits

✍ Scribed by Pan Soo Kim; Yangkok Kim

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 90 KB
Volume: 252
Category: Article
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(02)00020-0

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✦ Synopsis

Let G be a permutation group on a set Ω such that G has no fixed points in Ω. If, for a given positive integer m, the cardinalities |Γ g \Γ | is at most m for all g ∈ G and Γ ⊆ Ω, then G is said to have bounded movement m on Ω. When the maximum of |Γ g \Γ | over all g ∈ G and Γ ⊆ Ω is equal to m, we say G has bounded movement equal to m. We will show that if G has bounded movement equal to m and p ( 5) is the least odd prime dividing |G|, then it has at most 2m -(p -1) nontrivial orbits. Moreover the groups G attaining the maximum bound will be classified.

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